Researchers have introduced Σ-Mem, an online reliability memory framework designed to enhance coordination in LLM-based multi-agent systems by modeling agent competence rather than just interaction history. Unlike traditional memory systems, Σ-Mem tracks two types of evidence: individual historical competence for specific peers and peer-to-peer relationship evidence across the entire set. These are maintained as real symmetric states and updated dynamically using post-decision correctness feedback. A key technical innovation is the application of Weyl's inequality, which ensures that spectral changes during event-level updates remain bounded, allowing for stable online adaptation without requiring model retraining. The system offers a flexible interface supporting residual steering, response-free peer routing, and reliability-weighted voting. Evaluated across five Qwen-family models, Σ-Mem demonstrated robust performance by adapting to counterfactual reliability shifts and generalizing to previously unseen peers and task domains. Empirical results show that direct memory readouts outperform both majority voting and the most reliable fixed peer during out-of-distribution (OOD) evaluations. Furthermore, the system exhibits progressive improvement as more correctness feedback is ingested, proving that Σ-Mem effectively accumulates actionable reliability data to facilitate adaptive coordination in complex multi-agent environments.